Question

Boston Duck Tours is a firm that offers one-hour tours of the city of Boston using replica World War II amphibious vehicles. Suppose the wage for each employee is $20/hour and the amphibious vehicle rental rate is $100/hour. Each tour is staffed by one employee (who drives and narrates during the tour).

(a) Draw the set of isoquants that describe Boston Duck Tours’ production function for tours.

(b) Draw the set of isocosts that Boston Duck Tours faces.

(c) Find the cost-minimizing combination of K and L for Boston Duck Tours to produce 20 tours and show this on a graph. How much does it spend to produce 20 tours?

(d) This summer, Boston Duck Tours announced that all of its tours would be staffed by two employees (one to drive and one to narrate during the tour) due to safety concerns arising from recent crashes. As a result of this change, what is the new cost-minimizing combination of K and L and what is the new cost of producing 20 tours? Show the new cost-minimizing combination graphically.

Answer 1

(a) To provide the service of one tour, one driver and one bus is needed.

Thus, one driver and one bus is compulsory, without this combination, service cannot be provided.

Thus, the production function is Leontiff production function and is expressed as follows:

y = min(L,K)

Here, L is bus driver.

K is bus.

Graphically, production function is presented as follows:

The isoquant is L shaped if inputs are perfect complements.

(b) The wage of driver and tour guide for one hour tour =$20

The rent of bus for one hour tour service = $100

Thus, the cost of labor is $20 and the cost of capital is $100.

The cost function is:

C = WL + RK

C = 20L + 100K

The isocost line is presented below:

IC is the isocost curve.

(c) The cost function is:

C =WL+ RK

For 20 tours, 20 labors and 20 capital is needed.

C = (20)(20) + (100)(20)

C = 400 + 2000 = 2400.

The cost minimizing combination is one at which isocost line intersect isoquant:

The cost minimizing combination is one in which factor of production are used in fixed ratio.

(d) If two persons are needed for one tour then production function is:

y = min(2L, K)

The new cost function is:

C = 20 L + 100K

For providing 20 tour, cost incurred is:

C = 20(40) + 100 (20)

C = 800 + 2000 = 2800.

The new equilibrium is:

At the new equilibrium, input are consumed in ratio 2:1.

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