In our numerical example, Hamburger Heaven€™s expansion path requires K = L because w (the wage) and v (the rental rate of grills) are equal. More generally, for this type of production function, it can be shown that
K/L = w/v
for cost minimization. Hence, relative input usage is determined by relative input prices.
a. Suppose both wages and grill rents rise to $10 per hour. How would this affect the firm€™s expansion path? How would long-run average and marginal cost be affected? What can you conclude about the effect of uniform inflation of input costs on the costs of hamburger production?
b. Suppose wages rise to $20 but grill rents stay fixed at $5. How would this affect the firm€™s expansion path? How would this affect the long-run average and marginal cost of hamburger production? Why does a multiplication of the wage by four result in a much smaller increase in average costs?
c. In the numerical example in Chapter 6, we explored the consequences of technical progress in hamburger flipping. Specifically, we assumed that the hamburger production function shifted for q = 10ˆšKL to q = 20ˆšKL. How would this shift offset the cost increases in part a? That is, what cost curves are implied by this new production function with v = w = 10? How do these compare with the original curves shown in Figure?

d. Answer part c with the input costs in part b of this problem (v = 5, w = 20). What do you conclude about the ability of technical progress to offset rising inputcosts?

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Total costs Average and marginal costs Total costs $80 60 - 40 Average and 20 S1.00 marginal costs 0 20 40 60 80 Hamburgers per hour 0 20 40 60 80 Hamburgers per hour (a) Total costs (b) Average and marginal costs