pls do all parts asap.. thanks 5.2 a. The demand for chocolates ( of students is
ID: 1166680 • Letter: P
Question
pls do all parts asap..thanks
5.2 a. The demand for chocolates ( of students is given by the demand function p- 10-4x. The demand of chocolates by engineers is given by p 10-2x What is the market demand for chocolates (assume that the market consists of students and engineers only)? b. Besides Choco (whose supply function is equal to p x, see 4.2), there are two further producers of chocolates in the market. The supply functions of the other two producers of chocolates is given by p x. What is the market supply of chocolates? (Assumption: full competition). What is the equilibrium price for chocolates and how many chocolates are sold in the market? c. d. How large is the consumer surplus and the producer surplus and total welfare in the market?Explanation / Answer
a) Demand of chocolates by students: p = 10 - 4x
by engineers: p = 10 - 2x
Market demand for chocolates is horizontal summation of all demanding participants in the market. For given example, demanding participants are only students and engineers.
Thus, market demand of chocolate: p = (10 - 4x) + (10 - 2x)
Market demand function: p = 20 - 6x
b) There are total of three producers/suppliers of chocolates in the market. Each supplier has a supply function: p = x. Then, again, market supply function is horizontal summation of all individual supply functions or supply function of all supplying participants.
Thus, market supply of chocolates: p = x + x + x
Market supply function: p = 3x
c) Equlibrium point is where market supply equals market demand. Thus using parts (a) and (b), equilibrium occurs when, 20 - 6x* = 3x*
20 = 3x* + 6x*, giving market equilibrium x* = 20/9
At x* = 20/9, p* = 3*(20/9) (using market supply function), so p* = 20/3
Thus, equilibrium price for chocolates = 20/3, and (20/9) number of chocolates are sold in the market.
d) Cosumer surplus, CS = (1/2)*(x*)*(maximum willingness to pay - p*)
Maximum willingness to pay is found by putting x = 0 in the market demand function, so with x = 0, p = 20 - 6(0) = 20
Thus, CS = (1/2)*(20/9)*(20 - 20/3) = 400/27
Producer surplus, PS = (1/2)*(x*)*(p* - minimum willingness to receive)
Minimum willingness to receive is calculated by putting x = 0 in market supply function. So, with x = 0, p = 3(0) = 0
So, PS = (1/2)*(20/9)*(20/3 - 0) = 200/27
Total welfare in the market, TW = consumer surplus, CS + producer surplus, PS
TW = 400/27 + 200/27 = 600/27 = 200/9
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.