firm has a Cobb-Douglas production function q = f(K, L) = KαL 1−α and faces wages, w, and rental rate of capital, r. 1. Does this production function exhibit increasing, decreasing, or constant returns to scale? 2. Find the short-run cost curve, C(q), as a function of q and the parameters. 3. Assume that K = 10, r = 1.5, w = 6, and α = 2/3. Derive expressions for MC, VC, FC, ATC, AVC, and AFC. Plot MC, ATC, AVC, and AFC, all on the same graph. 4. Assume that K = 10, r = 1.5, w = 6, and α = 2/3. Assume now that we know the market price is p = 18, which is fixed, and we are still operating in the short-run. What is the profit-maximizing choice of q? 5. Solve for profits, π, as a function of market price, p (and the model parameters). Then, assume as we did in subpart 3 that K = 10, r = 1.5, w = 6, and α = 2/3. Will profits ever be negative? If so, find the price range at which profits are negative
A firm has a Cobb-Douglas production function q = f(K, L) = KαL 1−α and faces wages, w, and rental rate of capital, r. 1. Does this production function exhibit increasing, decreasing, or constant returns to scale? 2. Find the short-run cost curve, C(q), as a function of q and the parameters. 3. Assume that K = 10, r = 1.5, w = 6, and α = 2/3. Derive expressions for MC, VC, FC,
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