Joe’s Economics Assingment Help With Solution
Suppose that the Celis Sweets Company has a fixed proportions production function that requires it to use two sweet presses and one worker to produce 1000 sweets per hour.
1. Explain why the cost per hour of producing 1000 sweets is 2v + w ( where v is the hourly rent for sweets presses and w is the hourly wage).
2. Assume Celis can produce any number of sweets they want using this technology. Explain why the cost function in this case would be T C = q(2v + w), where q is output of sweets per hour, measured in thousands of sweets.
3. What is the average and marginal cost of sweets production ( again, measure output in thousands of sweets)?
4. Graph the average and marginal cost curves for sweets assuming v = 3, w = 5.
5. Now graph these curves for v = 6, w = 5. Explain why these curves have shifted.
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Trapper Joe, the fur trader, has found that his production function in acquiring pelts is given by q = √
H where q = the number of pelts acquired in a day, and H = the number of hours Joe’s employees spend hunting and trapping in one day. Joe pays his employees $8 an hour.
1. Calculate Joe’s total and average cost curves (as a function of q).
2. What is Joe’s total cost for the day if he acquires four pelts? Six pelts? Eight pelts? What is Joe’s average cost per pelt for the day if he acquires four pelts? Six pelts? Eight pelts?
3. Graph the cost curves from part a and indicate the points from part b. Explain why the cost curves have the shape they do.
Returning to the sweets producer problem, let’s look at the possibility that producing these delectable treats does not necessarily experience constant returns to scale.
1. In the problem, you showed that the cost function for sweets was given by T C = q(2v + w) where q is output of sweets (in thousands), v is the rental rate for sweet presses, and w is the hourly wage. Explain why this cost function illustrates constant returns to scale.
2. Suppose instead that the sweets cost function is given by T C = (2v + w)√q. Explain why this function illustrates increasing returns to scale. What does the graph of the total cost curve for this function look like? What do the implied average and marginal cost curves look like?
3. Suppose now that the sweets cost function is TC = (2v+w)q2. Explain why this function exhibits decreasing returns to scale. Illustrate this by graphing the total, average, and marginal cost curves for this function.
4. More generally, suppose TC = (2v + w)qs. Explain how any desired value for returns to scale can be incorporated into this function by changing the parameter s.
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