1. Consider a firm using labor and capital as its only inputs. The price of capi
ID: 1126010 • Letter: 1
Question
1. Consider a firm using labor and capital as its only inputs. The price of capital is $40 where the price of labor (wage) is $60. Using 500 units of labor and 500 units of capital the firm is producing 1200 units of output. At this mix of input, the firm's MPL is 10 while its MPK is 5.
a. Write the firm's isocost equation. What is the slope of the isocost?
b. Determine if the firm's mix of inputs is optimal. Explain.
c. If your answer to "b" is no, what should the firm do to improve its performance? Explain.
d. Now suppose as a result of a mandated increase in the minimum wage the wage increases to $80. What would be the implication of this change for this firm?
2. The following equation represents the weekly demand that a local theater faces.
Qd = 2000 - 25 P + 2 A,
where P represents price and A is the number of weekly advertisements.
Presently the theater advertises 125 times per week. Assuming this is the only theater in town, and its marginal cost, MC, is equal to zero,
a. Determine the profit maximizing ticket price for the theater.
b. What is the price elasticity of its demand at this price?
c. What is the elasticity of its demand with respect to advertising?
d. Now suppose the theater increases the number of its ads to 250. Should the theater increase its price following this ad campaign? Explain.
3. The Blue Dragon Restaurant is a new Chinese Restaurant in town. As the only Chinese restaurant in the area, it faces the following daily demand curve:
Q = 800 - 40 P
where Q is the number of meals it serves per day and P is the average price of its meals. The cost functions of the restaurant have been estimated as follows:
TC = 220 + 6Q + .02 Q2
MC = 6 + .04 Q
ATC = 220/Q +6 + .02Q ; Slope = -220/Q2 +.02
a. Determine the profit-maximizing price of each meal assuming The Blue Dragon is behaving as a monopoly.
b. Determine the profit of the Restaurant.
c. If the company were to produce as a perfectly competitive firm, how much would it produce?
d. What price should it charge as a competitive firm?
e. Would it still make a profit if it behaved like a competitive firm?
As a result of the success of the Blue Dragon other Chinese restaurants start appearing in the area. As the Blue Dragon's customers gradually start trying other (new) Chinese restaurants, its demand curve gets flatter (more elastic) and shifts to the left. In reaction, The Blue Dragon lowers its price and adjust its output to the point that, eventually, its (economic) profit disappears; It becomes equal to zero. At that point, the slope of its demand curve becomes -0.02.
f. Determine the new (equilibrium) average price The Blue Dragon charges for its meals.
g. Write the equation for this new (zero profit) demand curve.
Explanation / Answer
(a) Equation of isocost line = w.L+r.K=TC
where, w= wages
L= units of labour
r= cost of capital
K=units of capital
TC= Total Cost
Here the isocost equation will be 60L+40K=50,000
here Total Cost = 60X500+40X500= 50,000
Slope of isocost line = w/r= 60/40=1.5
(b) Optimal combination for the firm is attained where MPL/w=MPK/r
Since MPL/w=1/6 and MPK/r=1/8,
MPL/w>MPK/r, hence the optimal combination has not been attained.
(c) In order to improve its performance, the firm should employ more labour instead of capital, this process should continue till MPL/w=MPK/r.
(d) If minimum wages rise to $80, then the firm will attain euilibrium at the given units of labour (i.e. 500 units) as MPL/w=MPK/r=1/8
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