Question

4. There are three individuals in an economy. The demand functions for these individuals are given as

follows: X1 = 22-2P, X2 = 8-P, X3 = 28-2P. What is the market demand when P = 10?

(a) X = 30- 3P

(b) X = 50 -4P (c) X = 28 -2P (d) X = 36 -3P (e) X = 58- 5P

6. Best Buy sells Q units of áat-screen TVs each year. Best Buy executives also know that the price elasticity of demand for flat-screen TVs is eQ;P = -1.5. They propose a 20% reduction in the price of áat-screen TVs claiming that total revenue

   (a) will increase by 15%. (b) will increase by 30%. (c) will increase by 3:5%. (d) will decrease by 30%.

   (e) will increase by 4%.

Suppose the demand curve for beans is given by Q = 20- 2P . What price for beans yields highest total expenditures?

(a) 20 (b) 10 (c) 5

(d) 0
(e) cannot be determined with the given information.

Answer 1

a) when P=0, total market demand = X1+X2+X3= 22+8+28 = 58.

when P=1 total market demand is = 20+7+26= 53

so when price increases by $1, quantity demanded changes by 5 units. so the market demand equation is X=58-5P. when P=10 market demand is 8.

b) elasticity = % change in quantity demanded/ % change in price. Therefore, % change in quantity demanded = 1.5x20= 30%

Suppose the initial price is P and new price s P1. so % change in P is = P1-P/P x 100

which is equal to 20% reduction. (P1-P)/P x 100 = -20 P1= 8P/10

Similarly, Q is the initial quantity and Q1 is the new quantity demanded.

(Q-Q1)/Q x 100 = 30 Q1= 13Q/10

the new revenue is P1Q1= 104PQ/ 100 =1.04PQ

the % change in total revenue is =(1.04PQ- PQ)/PQ x 100 =4%. so total revenue increases by 4%.

C) the demand is Q= 20P-2. total expenditure in beans is PQ=20P-2P². differentiating PQ with respect to P and equating it to 0 we get 20-4P=0 which implies P=5