Question

How do we get the conditions? For example Xa > 0 if Px < 10 and Xb > 0 if Px < 5

8. There are 2 type-A and 4 type-B consumers in the economy. Each type-A consumer's demand for good X is described by the function XA 10-P. Each type-B consumer's demand for good X is described by the function X,-15-3Pn Please note that ХА and XB denote the quantity of good X demanded by type-A consumer and by type-B consumer, respectively. P denotes the price per unit of good X in euros. a) Describe the market demand for good X in this market by the market demand function(s) for good X (see "Market Demand" lecture notes!) (8 points) i ois ebs.ere number of type-A consumers n.-2 , demand function of type-A consumer XA-10-P, number of type-B consumers ns -4, demand function of type-B consumer Xn 15-3P 8. a) The market demand XM? Note that: XA > 0 if P.< 10 х..-0.kui P,210 and XB > 0, kui P.< 5 Xu-2rx^ + 4 x XB = 2 × (10-P.) + 4 x (15-3P-80-14P, if P.< 5

Answer 1

In this example, we need to find the market demand function.

Number of type A consumers = 2

Demand function of type A consumers for good X: X_A = 10 - P_X

Note that this demand is positive only if X_A > 0 => P_X < 10

Number of type B consumers = 4

Demand function of type A consumers for good X: XB = 15 - 3P_X

Note that this demand is positive only if XB > 0 => 3P_X < 15 => P_X < 5

• Thus, when P_X$\geq$ 10,

both type of consumers demand zero quantity of good and thus market demand X_M = 0

• If $5 \leq P_X < 10$ ,

only type A consumers have positive demand for it. Type B consumers demand zero.

Thus market demand = 2X_A (since there are two type A consumers in the market)

= 2*(10 - P_X) = 20 - 2P_X

• If $0 \leq P_X < 5$ , (assuming price will be positive, else consumers would want infinite quantity of good)

Both type A and type B consumers have positive demand for the good.

Thus market demand = 2X_A + 4X_B (since there are 2 type A consumers and 4 type B consumers in the market)

= 2*(10 - P_X) + 4(15 - 3P_X) = 20 - 2P_X + 60 - 12P_X

= 80 - 14P_X