Answer to Question #222727 in Macroeconomics for Rooth

Question

PRODUCTION FUNCTION IS

Q=200√L√K

PL=500

PK=800

TOTAL OUTLAY, C=5000

1).Determine lost minimizing combination of Labour and Capital

2.What is the cost minimizing output level

3.Construct the equilibrium for isoquant

4.if selling price of this product is Rs.200 per unit, what would be the profit or loss of this organization

Answer 1

1)

$Q=200\sqrt{L}\sqrt{K}\\MPL=200×\frac{\sqrt{k}}{2\sqrt{L}}\\=100×\frac{\sqrt{K}}{\sqrt{L}}\\MPK=200×\frac{\sqrt{L}}{2\sqrt{K}}\\=100×\frac{\sqrt{L}}{\sqrt{K}}\\$

$MRTS=\frac{MP_L}{MP_k}\\= \frac{100×\frac{\sqrt{K}}{\sqrt{L}}}{100×\frac{\sqrt{L}}{\sqrt{K}}}\\=\frac{K}{L}$

$MRTS=\frac{P_l}{P_K}\\=\frac{K}{L}=\frac{500}{800}=K=0.63L$

Cost function

$C=P_L\times L+P_K+K\\5000=500L+800K\\5000=500L+800(0.63L)\\5000=500L+504L\\L^*=5\\K^*=0.63(5)\\=3.2$

The optimal combination of labour and capital are (5, 3.2)

2)

The cost-minimizing output level is attained where an optimal combination of inputs is used to produce the output.

$Q=200\sqrt{5}\sqrt{3.2}\\=200\times2.2\times1.8\\=792$

The cost-minimizing output level is 792 units.

3)

The equilibrium is attained where isoquant is tangent to the isocost line. The isoquant shows the different combinations of inputs that can produce the same level of output. The isocost curve shows the different combinations of inputs that can be purchased with the given cost of inputs and income of the firm.

4)

$200\times 792=RS158400$

The profit$=158400-5000=Rs153400$