1. Short questions:
(a) If p · MP1 > w1, (where p is the output price, MP1 the marginal product of factor 1, and w1 the rental rate of factor 1), should the firm increase or decrease the amount of factor 1 in order to increase profits? Explain.
(b) If a firm had everywhere increasing returns to scale, what would happen to its profits if prices remained fixed and if it doubled its scale of operations? Show your work.(c) A firm is currently earning negative profits on each good it produces. Claim: it is always optimal for this firm to shut down production in the short run. True or false?(d) As long as the marginal cost of production
2. Consider the firm ACME which uses capital, K, and labour, L, to produce widgets according to the following production function: f(K, L) = K23 L13 . Let r and w be the prices of capital and labour respectively. P is the price of widgets. The markets for widgets, capital, and labour are all perfectly competitive.
(a) What is the technical rate of substitution between capital and labour for ACME?
(b) In the short run, the level of capital is fixed at K = K. Set up the short run profit maximization problem. Calculate the short run optimal level of labour.
(c) In the long run, ACME can vary both K and L. Set up ACME's long run cost minimization problem by using the Lagrange method. What are the cost minimizing levels of K and L in the long run?
(d) Derive ACME's long run cost function.
3. Ricardo produces widgets, using as inputs labor (L) and machines (K). His production function is given by the following equation:y = 10K^2/3 + L^1/2.
(a) What type of returns to scale (increasing/constant/decreasing) does Ricardos production function exhibit? Explain.At the end of last year, Ricardo bought his only machine for $1,000. He will use this machine for 5 years,after which the machine will have no value. Ricardo will calculate depreciation linearly (depreciationwill be 20% of the initial value of the machine per year). This machine has no other use besides Ricardosproduction of widgets, and, at this moment, Ricardo cannot buy any more machines.
(b) What is Ricardos annual fixed cost of production? Is the fixed cost sunk or not? Explain.
(c) What is Ricardos demand for labor as a function of the quantity he wants to produce annually?
(d) Assuming that wage equals 1, what is Ricardos annual total cost function?
4. Sallys firm produces granola bars with a fixed cost of 10 (this cost is already sunk). Her variable cost function is V C = y^2 + 2y.
(a) Assuming the market for granola bars is competitive, derive Sallys supply function.
(b) What is Sallys revenue if the market price is 6? What is her profit? Does she want to stay in this market? Explain.
5. In Freedonia, a single firm is in the domestic steel business. It sells steel at $680 per ton, well above thewold price of $375 per ton. The firm is protected against foreign competition by incredibly high tariffsthat ban all imports.The firm has never exported steel. The CEO argues: "The average cost of manufacturing steel, whichvaries with the rate at which the firm produces steel, is never below $400 per ton. We simply cannotmake positive profits selling steel for $375 per ton." Is this argument convincing? Provide a short answer(at most 4 sentences).