Determine the long-run total, average and marginal cost
functions of the firms having the
production functions and facing the input prices given below:
a. ?=f(K,L)=√K+2√L,PK=1,PL=2
b. Q=f(K,L)=K+L,PK=2,PL=1
c. Q=f(K,L)=K1/2L1/2,PK=2,PL=2
Determine the long-run total, average and marginal cost functions of the firms having the production functions...
For a constant cost industry in which all firms the same cost functions, their long-run average cost is minimized at $10 per unit output and 20 units (i.e. q = 20). Market demand is given by QD=DP=1,500-50P. Find the long-run market supply function Find the long-run equilibrium price (P*), market quantity (Q*), firm output (q*), number of firms (n), and each firm’s profit. The short-run total cost function associated with each firm’s long-run costs is SCq=0.5q2-10q+200. Calculate the short-run average...
Short Run Cost Curves: Consider two firms, producing different products, with the following production functions: q=5KL (1) q=5(KL).5 (2) a. For a short-run situation in which K=100, and given wage = 3 and cost of capital = 1, derive expressions short run total cost for each production function. (Start by using the production function to develop an expression for L in terms of q, and then substitute that, and the given parameters, into the generic expression for Total Cost =...
Let K be the level of capital in the short run. The prices of capital and labor are r = 10 and w-5, respectively. For each of the following production functions, (1) derive the short-run cost function (5 pts), (2) derive the long-run cost function (5 pts), and (3) illustrate how you derive the long-run cost function with isoquants and isocosts (5 pts). Hint: for the long-run cost function, first set up the cost minimization problem. (a) (15 pts) f(K,...
Given the following long run production and cost functions: q=LPK1/4 C = 12L +4K (A) What input has diminishing marginal returns? (B) Does this production function display increasing, decreasing or constant returns to scale? (C) What is this firm's expansion path assuming input prices do not change? Clearly type out your answer to parts (A), (B) and (C) in the space provided. Retain all of your handwritten work for this question to be uploaded separately after you have completed the...
For each of the long-run total cost functions given below, determine the average cost function and state what type of returns to scale the firm experiences: a. ?RTC = 100Q b. ?RTC=3Q2+Q c. LRTC=200Q−Q2
Given the following long run production and cost functions: q=L3K1/4 C = 12L +4K (A) What input has diminishing marginal returns? (B) Does this production function display increasing, decreasing or constant returns to scale? (C) What is this firm's expansion path assuming input prices do not change?
Explain why the industry supply curve is not the long-run industry marginal cost curve. The industry supply curve is not the long-run industry marginal cost curve because O A. production will only occur along the long-run marginal cost curve for prices above average variable cost. O B. at prices above the minimum long-run average cost of production, firms will exit the industry. O C. production will only occur along the long-run marginal cost curve when profits are earned. O D....
Given the following long run production and cost functions: 4 = 1/3K2 C = 15L + 3K (A) What input has diminishing marginal returns? (B) Does this production function display increasing, decreasing or constant returns to scale? (C) What is this firm's expansion path assuming input prices do not change? HTML Editora
1. Graph the short-run total product curves for each of the following production functions if K is fixed at Ko 4 (a) Q = F(K, L) = 2K + 3L. (b) Q = F(K, L) = K2L2. (c) In the long run, are the above two production functions characterized by constant returns to scale, increasing returns to scale, or decreasing returns to scale?
(2) Consider the following production function: f(k.) 10k. k+ (a) Derive the conditional input demand functions. (b) Derive the long-run total cost, marginal cost and average cost functions. (c) State and verify Shephard's lemma for the functions derived in (a) and (b). (d) When wx = 4 and we = 1, plot the long-run total cost, average cost and marginal cost functions.