Author Question: Suppose the current price and quantity of widgets is p = 50 and Q = 125. The demand for widgets ... (Read 38 times)

notis · **on:** Jul 1, 2018

Suppose the current price and quantity of widgets is p = 50 and Q = 125.

The demand for widgets is log-linear and the price elasticity of demand is E = -2. The supply of widgets is perfectly elastic.
a. Derive the equations for the demand and supply of widgets.
b. What would be the effect on the equilibrium price and quantity if demand were to increase by 500 widgets?

Question 2

The following table shows the relationship between output and number of workers in the short run. If the wage is 50/day, find marginal cost of production.

Number of Workers Output
0 0
1 50
2 110
3 300
4 450
5 590
6 665
7 700
8 725
9 740
10 735

tranoy · **Reply #1 on:** Jul 1, 2018

Answer to Question 1

a. Because demand is log linear, the demand equation is of the form Q = Ape, where A is a positive constant and e is the price elasticity of demand. We can solve for A:
125 = A(50 )-2 A = 312,500
Demand is then given by Q = 312500p-2
Supply is horizontal and so the equation is p = 125.
b. An increase in demand will lead to Q = 313,000 and p = 125

Answer to Question 2

Number
of Workers Output MPL MC (=w/MPL)
0 0 -- --
1 50 50 1.00
2 110 60 0.91
3 300 190 0.26
4 450 150 0.33
5 590 140 0.36
6 665 75 0.67
7 700 35 1.43
8 725 25 2.00
9 740 15 3.33
10 735 -5 --