2) In a competitive market for a certain procuct, the quantities demanded and su
ID: 1137802 • Letter: 2
Question
2) In a competitive market for a certain procuct, the quantities demanded and supplied at various price are as follows: Price 30 Su 30 28 26 24 24 26 28 60 a) Calculate and interpret the price elasticity of demand when the price increases from $40 to $50 b) Calculate and interpret the price elasticity of supply when the price increases from $40 to $50. c) What are the equilibrium price and quantity? d Suppose the government sets a price ceiling of $40. Is there any shortage or surplus? If there is, how large will it be? e) What will be the economic impacts of the price ceiling in Part d) caused by the shortage or surplus if there is any? 3) Dannielle receives utility from days spent traveling on vacation domestically (D) and days spent taveling on vacation in a foreign country (F), as given by the utility function UD, - 100D F. Also, the pice of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Dannielle's annual travel budget is $4000. a) Ilustrate the indifference cucve associated with a utility of 1000000 and the indifference curve associated with a utility of 1210000. Hint To find the nature of the curve, use the following link TT.Wolfra / and write vor equation that vou want to sketch as follows: grapb 1000000100D F, F 0, D>0. Reprodice the curve you see in the first quadrant only since we do not care about negative quantities in Economics. Repeat the process when the utility is 1210000. Please, do NOT copy and paste the curves from www.wolframalpha.com. It should only provide you guidance on the nature of the curves. Reproduce the cucves yourself] b) Graph Dannielle's budget line on the same graph. [Hint Include the budget constraint in Wolfram Alpha. Separate all equations with commas ()] Can Dannielle afford any of the bundles that give her a utility of 1000000? What about a utility of 1210000? Why? Why not? d) Find Dannielle's utility-maximizing choice of days spent traveling domestically and days spent in a foreign country from the original budget. Hint: MU 200DF and MU 200D F e Calculate Dannielle's utility at the cons tion bundle found in Part d)Explanation / Answer
A) Price elasticity of demand=
percent change in quantity /percent change in price
Percent change in quantity= change/average *100
= 26-28/(26+28÷2)*100
= -2/27*100
= - 0.074*100 = -7.4%
Percentage change in price= change /average * 100
= 50-40/(50+40÷2)*100
=10/45*100
= 22.22%
Price Elasticity of demand= -7.4/22.22= 0.033
Inelastic demand since the value of elastocity is less than 1.
B)
Price elasticity of supply=
percent change in quantity /percent change in price
Percent change in quantity= change/average *100
= 26-24/(26+24÷2)*100
= 0.08 *100=8%
Percentage change in price= change /average * 100
= 50-40/(50+40÷2)*100
=10/45*100
= 22.22%
Price Elasticity of demand= 8/22.22= 0.36
Inelastic supply. Since the value of elasticity is less than 1.
C) Equilibrium Price and Quantity is decided where demand is equal to supply.
At price 50 both demand and supply is 26.
So Equilibrium price* =50
Equilibrium Quantity*=26
d) If the government sets a price ceiling of $40 when equilibrium is price $50.
At price $40
Demand=28
Supply= 24
Since demand is more than supply there will be shortage.
Supply-demand=24-26= -2 million shortage.
E) There is a price ceiling which led to shortage in the market.
It will lead to less supply of goods by the producers as they are getting less price. Producers may leave the industry. There will be few consumers who will not get the good. Consumers may switch to other good.
There will be queue in line for the good, government may start rationing of the good since there is shortage and not everybody's demand can be met or there may be an emerging black market.
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