Hello, the solutions posted below were provided by my professor. I\'m having a h
ID: 1216828 • Letter: H
Question
Hello, the solutions posted below were provided by my professor. I'm having a hard time understanding where any of this is actually coming from. I've been reading my textbook but it doesn't provide the formulas that the professor is using to solve each of the sub qustions. I was hoping someone would be able to explain each part of the question in more detail! Thanks!
There are 2 firms in the market and each of them plans the production as Q KIBLIs, where K is capital and L labor. Given K-8, capital rental rate R-0.5, and wage W-8, answer the following questions if the market demand function is Q(P+2)1 1. What is the supply relation by a firm? 2. What is the labor demand relation by a firm? 3. Can you derive the variable cost of a firm? 4. What is the total cost of a firm? 5. What is the cost of producing more units of good? 6. In equilibrium, what is the supply function of a firm? 7. What is the total supply function of the economy? 8. What is the equilibrium price for goods? 9. What is the equilibrium quantity of goods? 10. How much labor will a firm demand? 11. What is the revenue of a firm?Explanation / Answer
1) Production Function Q = K1/3 L 1/3............(1) is actually the supply equation which states that Q amount of output will be produced using K1/3 units of capital and L 1/3 units of labor.
Value of K = 8, substitute this in equation 1
Q = 81/3 L 1/3
Cube root of 8 = 2, Q = 2L 1/3 .......(2)
2) Labor demand equation should be such that L is in left hand sife as dependent variable. Rearrange equation (2)
L 1/3 = Q/2 Put value of Q from equation 1
L = ( Q/2 ) 3
L = Q3/8 ......(3)
3) Rental rate is fixed while wages depend on quantity of labor
Variable Cost = wL where w = 8 and L = Q3/8
VC = 8 x Q3/8 = > Q3
4) Total Cost if sum of fixed and variable cost = rK + wL
where r = 0.5 ; K = 8 and wL = Q3
TC = 0.5 x 8 + Q3 => 4 + Q3
5) Cost of producing more untis is marginal cost which is differentiation of total cost with respect to quantity.
MC = dTC / dQ => d (4 + Q3 ) / dQ => 0 + 3Q3 -2
MC = 3Q2
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