Information About Case
Allen Bond opening own construction business (builds garages for residential homes)
By 1985 the company had 20 employees ($25k annual salary/ per employee)
400 – amount of garages built
Materials are provided by the customer
$1,600 how much each garage sells for
Firm has a large stockpile of capital equipment (trucks, tools, instruments, etc.)
Measure of unit for capital: one truck, a ladder, power tools, and an air compressor
1 unit costs $5,000/ yr – rent
Used 15 units during 1985
$100k – inheritance to start business
$300k – how much he can sell the business for
$15K – profit after salary
14% per annual – Market interest rate
40K – amount of money that he will get paid annually with other job
Fixed Costs (TFC):
Forgone earnings: 40K
Opportunity cost of selling price: 300K
Labor – (20 carpenters / $25k annually)
Capital – ($5,000/annual for rent)
Price of Output
Garages ($1600/garage or $64,000)
Problems to Consider
Is Bond Construction actually being profitable?
Is the current mix of capital and labor optimal?
Determine the true economic profit earned by the firm in 1985
The true economic profit earned by Allen Bond’s firm in the year 1985 was $-17,000. This answer was calculated using the equation; economic profit = total revenue-economic cost. The total revenue is equal to the price of the product multiplied by the quantity of the product that was sold was. The opportunity cost is equal to the foregone selling price of the firm multiplied by the market interest and the foregone salary of a new job. The accounting cost is equal to the wage of the workers multiplied by the number of workers plus the profit after giving Mr. Bond his salary for the year.
Economic profit = total revenue-economic cost
Total revenue= price x quantity
Economic cost = accounting cost + opportunity cost
(1,600 x 400)-[(300,000*.14)+((25,000*20)+115,000+40,000)]
-57,000 = 640,000 – (42,000 + 500,000 +115,000 +40,000)
(P*Q) – (opportunity cost + accounting cost)
Economic profit= -57,000
B. If the economic profit was negative in 1985, determine the output needed to breakeven. You will need to determine the relevant total and per unit cost, and marginal cost functions.
The break even amount that would be needed if the economic profit was negative in 1985 is 3,400 products. This was calculated using the equation: QBE = TFC/ (P- AVC). The TFC (total fixed cost) is the selling price offered to Mr. Bond for the firm he started and the salary that is being offered to him that he is foregoing each year when he decides to stay with the firm. The fixed cost equals $340,000. The variable costs (VC) is the sum of the salaries of the workers multiplied by the number of workers including Mr. Bond, and the price of one unit of capital multiplied by the number of capital the firm rented that year. The variable costs equals 600,000. The variable cost was used to find the average variable cost (AVC) within the equation AVC = VC/ Q. The AVC is equal to 1500.
The marginal cost was calculated using the equation MC = ????TC / ????Q. The change in the total cost and quantity was found using the changes in their amount from the year 1984 and 1985.
TC = FC +VC
FC = 40000 +300000 = 340000
Selling price and forgone earnings
VC = 525000 + 75000 = 600000
Rent and workers
QBE = TFC/ (P- AVC) = 340000/ (1600 – 1500) = 3400
AVC = VC/Q = 600000/400 = 1500
MC = change in TC/ change in Q
1544.71544 = 190000 / 123
Change in Q = 123
Change in TC = change in VC + FC
190000 = [(3*5000)+(7*25000)] + 0
C. Determine whether returns to scale are increasing, decreasing, or constant. Explain.
The returns to scale is constant. Alpha is 0.19 and beta is 0.81. 0.81+.019 is equal to 1, making it constant returns to scale.
Q= AKL, where A>0, 0< ,general Cobb-Douglas Function
????+????=1 constant returns to scale
????+????<1 decreasing returns to scale
????+????>1 increasing returns to scale
Q=20K0.19L0.81, Bond Case Function
0.19 + 0.81 = 1 , constant returns to scale
D. Determine the optimal (that is, the profit maximizing) mix of labor and capital that should be used to produce 400 units of output. Compare this mix to the actual combination of labor and capital used in 1985. Note: For a Cobb-Douglas production function, the equations for the marginal products of labor and capital respectively are: MPL = bAKaLb and MPK = aAKa-1Lb
MPL/PL= MPK/ PK
16.2K0.19L-0.19/ 25,000 = 3.8K-0.81L0.81/ 5,000
16.2K0.19/ 25,000L0.19 = 3.8L0.81/ 5,000K0.81