## Microeconomics-Q2 Online Services

1. Suppose the production function for widgets is given by: q = kl – 0.8k2 – 0.2l2, where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input. Suppose k = 10. The average product of labor of labor reaches it maximum when units of labor input are used. At that point, the number of widgets produced is units. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. Hints: This is the fill in the blanks version of problem 9.2, and it is similar to example 9.1.)

5 points

**QUESTION 2**

1. Suppose the production function for widgets is given by: q = kl – 0.8k2 – 0.2l2, where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input. Suppose k = 10. (You are encouraged to graph the total product, marginal product of labor and average product of labor curves.) Which of the following statements is not correct?

a. The average product curve crosses the marginal product curve at its maximum level of average product of labor.

b. The total product reaches its maximum at the level at which the average product of labor is at its maximum level.

c. The total product reaches its maximum at the level at which the marginal product of labor is equal to zero.

d. When the average product of labor decreases, the marginal product of labor is less than the average product of labor.

5 points

**QUESTION 3**

1. Suppose the production function for widgets is given by: q = kl – 0.8k2 – 0.2l2, where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input. Which of the following statements is correct?

a. The widget production function exhibits constant returns to scale.

b. The widget production function exhibits increasing returns to scale.

c. The widget production function exhibits decreasing returns to scale.

d. The widget production function is homogeneous of degree 1.

5 points

**QUESTION 4**

1. Implicit costs might include

a. labor costs

b. capital costs

c. entrepreneurial services costs

d. b and c

5 points

**QUESTION 5**

1. Suppose that a firm is using quantity k of capital input and quantity l of labor input to produce output level q0. Further suppose that, at this input combination, the rate of technical substitution (RTS) is 2. Assume also that w = $1 and v =$1, where w and v are the rental rates at which this firm buys its labor and capital services. This firm can reduce its cost of producing output level q0 by

a. reducing labor input use by 1 unit and increase capital input use by ½ unit.

b. reducing labor input use by 2 units and increase capital input use by 1 unit.

c. reducing capital input use by 2 units and increase labor input use by 1 unit.

d. reducing capital input use by 1 unit and increase labor input use by 1 unit.

5 points

**QUESTION 6**

1. A firm production function is given by q = f(k,l) = k•l. q0 = 100. w = $20, v = $5. At the point at which this firm minimizes the cost of producing q0, it uses unit(s) of labor and unit(s) of capital. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. HINT: see chapter 10.)

5 points

**QUESTION 7**

1. A firm production function is given by q = f(k,l) = k•l. q0 = 100. w = $20, v = $5. The value of the Lagrange multiplier λ associated with the cost minimizing input choice is [λ]. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. HINT: see Example 10.1 in your text.)

5 points

**QUESTION 8**

1. A firm production function is given by q =f(k,l) = k•l. This firm demand equation for capital input k, in terms of q, w, and v, is given by the following equation: k* = [q(w/v)]n, where power n is equal to [n]. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. HINT: see Example 10.2 in your text.)

5 points

QUESTION 9

1. A firm production function is given by q =f(k,l) = k•l. Derive this firm (indirect) cost function. Using this firm (indirect) cost function, compute its total cost of production when q0 = 100, w = $20, v = $5. It is equal to [c] dollar(s). (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. HINT: see Example 10.2 in your text.)

5 points

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**QUESTION 10**

1. Which of the following statements is correct?

a. Large values of elasticity of substitution s indicate that firms change their input proportions significantly in response to changes in relative input prices.

b. Low values of elasticity of substitution s indicate that firms change their input proportions significantly in response to changes in relative input prices.

c. Large values of elasticity of substitution s indicate that changes in input prices have relatively little effect on the input proportions used by firms.

d. Values of elasticity of substitution s equal to 0 indicates that firms change their input proportions significantly in response to changes in relative input prices.

5 points

**QUESTION 11**

1. Consider the following firm (indirect) cost function: C(v,w,q) = 2(q•v•w)0.50. At q0 = 100, w = $20, v = $5, the (contingent) quantity demanded for labor input lc is [lc]. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. HINTS: Use the Shephard lemma to derive this firm contingent demand function for labor input. See Example 10.4 in your text.)

5 points

**QUESTION 12**

1. Suppose a firm faces the following demand for its output q: q = 100 – 10p, where p represents the price it receives per unit sold. Assume this firm marginal cost is MC = 4. The level of output at which this firm maximizes its profit is . (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. Hint: see Example 11.1.) The price charged at this firm’s profit maximizing level of output is .

5 points

**QUESTION 13**

1. Suppose a firm faces the following demand for its output q: q = 100 – 10p, where p represents the price it receives per unit sold. Assume this firm marginal cost is MC = 4. The absolute value of the price elasticity of demand at this firm’s profit maximizing level of output is . The markup over marginal cost, or Lerner Index, at this firm’s profit maximizing level of output is percent. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. Hint: see Example 11.1.)

5 points

QUESTION 14

1. Which of the following statements is correct?

a. Long-run total costs are the sum of fixed costs and variable costs.

b. Short-run total cost curves are an “envelope” of their respective long-run curves.

c. Long-run total cost curves are an “envelope” of their respective short-run curves.

d. None of the above.

5 points

**QUESTION 15**

1. A firm production function is given by q = f(k,l) = k•l. w = $20, v = $5. Consider a short-run situation where the level of capital is fixed at k1 = 10. The short-run total costs for producing q0 = 100 is equal to [sc]. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. HINT: See Example 10.5 in your text.)

5 points

**QUESTION 16**

1. Which of the following statements is correct?

a. The firm’s profit maximizing level of output will be found only in the elastic portion of the linear demand facing the firm.

b. The firm’s profit maximizing level of output will be found only in the inelastic portion of the linear demand facing the firm.

c. The firm’s profit maximizing level of output will be found either in the elastic or the inelastic portion of the linear demand facing the firm.

d. The firm’s profit maximizing level of output will be found at the point where the linear demand facing the firm is unit-elastic.

5 points

**QUESTION 17**

1. Which of the following statements is correct?

a. The demand curve facing a price-taking firm is its average revenue curve.

b. The demand curve facing a price-taking firm is a horizontal line through the prevailing market price.

c. The demand curve facing a price-taking firm is its marginal revenue curve.

d. All of the above

5 points

**QUESTION 18**

1. Which of the following statements is correct?

a. The positively sloped portion of a price-taking firm’s short-run marginal cost curve, above its point of minimum short-run average variable cost, is this firm’s short-run supply curve.

b. In the short-run, for prices below SAVC, the price-taking firm will choose to produce no output.

c. In the short-run, a price taking firm will produce level of output for which SMC = p, where p is the market price at which it sells its output.

d. All of the above

5 points

**QUESTION 19**

1. A firm production function is given by q = f(k,l) = k•l1/2. w = $20, v = $5. Consider a short-run situation where the level of capital is fixed at k1 = 10. At p = $12, in the short-run, the quantity supplied by this price-taking firm is equal to [q]. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. HINTS: First, derive this firm short-run total cost function. Next, compute its short-run marginal cost function. Finally, use the short-run profit maximization rule to derive its short-run supply equation. See Examples 10.5 and 11.3 in your text.)

5 points

**QUESTION 20**

1. A firm production function is given by q = f(k,l) = k•l1/2. Consider a short-run situation where the level of capital is fixed at k1. This firm’s profit function is of the form Π(p,v,w,k1) = awbpck1d – vk1, where factor a is equal to [a]. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. HINT: See Example 11.4 in your text.)

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