Part - 1
Question 1:
1. If a perfectly competitive industry consisting of identical rms is in long run equilibrium and the market demand increases, with nothing else changing, then in the new long run equilibrium individual rm output will be higher.
2. The unconditional (pro t maximizing) factor demand for an input equals the conditional factor demand for the same input at the pro t maximizing output quantity.
3. If average variable cost is decreasing then marginal cost is decreasing.
4. The long run e ect of a quantity tax imposed on a competitive industry is that consumers end up paying the whole tax amount.
5. It is possible to have a Pareto ecient allocation in which someone is worse o than he is at another allocation that is not Pareto ecient.
Question 2:
A competitive software rm has a production function f(x1; x2) = px1x2 where x2 is the number of computers and x1 is number of workers employed. Let the workers' wage be w1 = 4, the computer price is w2 = 16; and output price be p = 4: Suppose that in the short run the rm can only vary the amount of workers it employs but not the number of computers and that the latter is xed at x2 = 4 in the short run.
(a) Derive the rm's short run conditional factor demand for workers if the rm wants to produce y units of output. What is the rm's short run cost function for producing output y?
(b) What are the rm's xed costs, average variable costs, average costs and marginal costs of producing output y? Sketch the AC, AVC and MC curves on a graph.
(c) What is the rm's short run supply curve? What is the pro t maximizing amount of output that the rm will produce in the short run? At this output level how much pro ts/losses does the rm make?
Suppose now that the rm is in the long run and can vary both its factors of production.
(d)What are the rm's long run conditional factor demands for producing y units of output? What is its long run cost function? What is its long run supply curve?
(e) Assuming that input and output prices remain at their given short run levels in the long run as well, how much would the rm produce in the long run?
Part-2
A rm has a production technology involving two inputs, capital (K) and labor (L), f(K; L) = K1=3 L1=3. The price of capital is r; the price of labor is w, and the output price is p. Let r = 1 and w = 9.
Assume rst that both inputs are variable.
(a) Derive the rm's conditional factor demands for producing y units of output, K(y) and L(y). What is the rm's cost function c(y)? What are the average and marginal cost functions?
For any output price p, derive the rm's long run supply function y = S(p).
(b) If p = 9 how much output will the rm produce and how much pro ts would it make? Now assume that in the short run the rm's quantity of capital is xed at K = 1:
(c) What is the conditional factor demand for labor for producing y units of output? What is the short run cost function of the rm, cSR(y)? What are the short run average and marginal cost functions? Are there any xed costs? For any output price p derive the rm's short run supply function y = SSR(p).
(d) For what output quantity, y ; is K = 1 the optimal long run level of capital? Show that the long run average cost curve (from part a) and the short run average cost curve (from part c) are tangent at y = y . Explain why.
Part 3
Suppose that wheat is produced under perfectly competitive conditions and market demand for wheat is D(p) = 410 10p. Individual wheat farmers all have identical long run cost functions c(y) = 64 + y + y2 where y is the amount of output they produce.
(a) How much would each farmer produce in the long run? How many farmers would exist in the industry in the long run?
(b) Now suppose that the demand for wheat falls to D2(p) = 330 10p: What will be the short run price of wheat (i.e. when the number of farmers and farmers' outputs are xed)?
How about the new long run price? What will be the new equilibrium number of farmers in the industry in the long run?