The production of Kumquats requires two inputs: labor and machines (capital). To
ID: 1192053 • Letter: T
Question
The production of Kumquats requires two inputs: labor and machines (capital). Total costs associated with producing a given level of Kumquats is given by:
TC = Wl L + WkK (1)
Where:
TC = Total cost
Wl = wage rate of labor
Wk = wage rate of capital
L = quantity of labor
K= quantity of capital
Assume that the wage of labor is equal to $2 and that the wage of capital is equal to $4. Furthermore, assume that total cost is equal to $200.
Question: Assume that costs are identical to what is given above. But, production is given by:
Q = L + 3K (3)
Note: L and K are prefect substitutes for each other.
a. Solve for L, K, and Q. Show all mathematical steps.
b. In a graph, draw the isoquant and iso-cost curve. Label the equilibrium quantity of labor and capital. Label the endpoints associated with the cost curve.
Explanation / Answer
TC= w.L +r.K
w=2, r=4, TC=200
Thus, 200=2L+4K
Now, Q = L + 3K. Thus, L and K are prefect substitutes.
Case1,
L=0. Thus, 200=2.0+4.K or 200=4K or K=50.
In that case, Q=0+3.50=150
Case 2,
K=0. Thus, 200=2.L+4.0 or 2L=200 or L=100.
In that case, Q=100+3.0=100
Both in cases 1 & 2, the cost is 200 but the output produced is more in case 1. Thus case 2 is not possible.
Hence, in equilibrium
L=0, K=50, Q=150
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