1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when:

(a) L=1, (b) L=10, (c) L=100, (d) L=1000

Does the law of diminishing marginal productivity apply to this particular function?

2. Show that the price elasticity of demand is constant for demand functions of the form

where A and n are positive constants.

3. The demand and total cost functions of a good arerespectively and

a) Find expressions for TR, (profit) , MR, and MC in terms of Q.

b) Solve the equation

and hence determine the value of Q which maximizes profit.

c) Verify that, at the point of maximum profit, MR=MC.

4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components:

(a) GH¢10 million for the land

(b) GH¢1/4 million per floor

(c) Specialized costs of GH¢10000x per floor.

How many floors should the office complex contain if the average cost per floor is to be minimized?

5. The supply and demand equations of a good are respectively given by and

The government decides to impose a tax, t, per unit. Find the value of t (in Ghana cedis) which maximizes the governments total tax revenue on the assumption that equilibrium conditions prevail in the market.

6. A firm's demand function for a certain good is given by. Its total cost function is . What output level maximizes the firm's profit?

7. An individual’s utility function is given by

where is the amount of leisure measured in hours per week and is income earned measured in cedis per week.

Determine the value of the marginal utilities, when = 138 and = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?

8. A firm’s total cost function is given by

Where and denote the number of items of goods 1and 2, respectively that are produced. Using the substitution method, find the values of and which minimize costs if the firm is committed to producing 40 goods of either type in total.

9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function

where and denote the quantity of items of goods 1and 2, respectively that are produced. If P1 and P2 denote the corresponding prices then the demand equations are

Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.

Question

1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when:

(a) L=1, (b) L=10, (c) L=100, (d) L=1000

Does the law of diminishing marginal productivity apply to this particular function?

2. Show that the price elasticity of demand is constant for demand functions of the form

where A and n are positive constants.

3. The demand and total cost functions of a good arerespectively and

a) Find expressions for TR, (profit) , MR, and MC in terms of Q.

b) Solve the equation

and hence determine the value of Q which maximizes profit.

c) Verify that, at the point of maximum profit, MR=MC.

4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components:

(a) GH¢10 million for the land

(b) GH¢1/4 million per floor

(c) Specialized costs of GH¢10000x per floor.

How many floors should the office complex contain if the average cost per floor is to be minimized?

5. The supply and demand equations of a good are respectively given by and

The government decides to impose a tax, t, per unit. Find the value of t (in Ghana cedis) which maximizes the governments total tax revenue on the assumption that equilibrium conditions prevail in the market.

6. A firm's demand function for a certain good is given by. Its total cost function is . What output level maximizes the firm's profit?

7. An individual’s utility function is given by

where is the amount of leisure measured in hours per week and is income earned measured in cedis per week.

Determine the value of the marginal utilities, when = 138 and = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?

8. A firm’s total cost function is given by

Where and denote the number of items of goods 1and 2, respectively that are produced. Using the substitution method, find the values of and which minimize costs if the firm is committed to producing 40 goods of either type in total.

9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function

where and denote the quantity of items of goods 1and 2, respectively that are produced. If P1 and P2 denote the corresponding prices then the demand equations are

Using the Lagrange multiplier approach, find the maximum profit if the firm is contracted to produce a total of 15 goods of either type. Estimate the new optimal profit if the production quota rises by 1 unit.

Accepted Answer

Suppose the given equation is:
Q = 50L - 0.01L2
The formula to find MPL = aQ/ aL 
50 - 0.02L2-1
50 -…