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If the domestic demand curve is Equal 20p Superscript negative 0.5​, the domestic supply curve is Equal 5p Superscript 0.5​, and the world price is ​$7.00​, use calculus to determine the changes in consumer​ surplus, producer​ surplus, and welfare from eliminating free trade. The change in consumer surplus ​(Upper Delta​CS) from eliminating free trade is ​$ nothing. ​(Enter your resp

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4 votes

Answer:

$52

$ 1.33

  • consumer price will increase
  • consumer surplus will decrease
  • import will decrease
  • reduced export
  • portends gloom for the general outlook for the economy

Step-by-step explanation:

Given domestic demand curve, S(p) = 20p⁻⁰°⁵

the domestic supply curve S(p)= 5p⁰°⁵

world price is ​$7.00

using calculus to determine the changes in consumer​ surplus

by consumer surplus means in this case supply exceeds demand

we establish the equilibrium point where the supply and demand functions meet or are equal

solving 20p⁻⁰°⁵ = 5p⁰°⁵

20/5 = p⁰°⁵/p⁻⁰°⁵

4 = p⁰°⁵⁺⁰°⁵

4= p = q which is the quantity produced

consumer surplus = maximum price willing to pay - Actual price

= ∫⁴₀ dp dp - p* q

= ∫⁴₀20p⁻⁰°⁵ dp- 7* 4

= 20∫⁴₀p⁻⁰°⁵ dp -28

= 20/0.5 p⁰°⁵- 28

= 40 *4⁰°⁵ - 28 = $52

producer surplus = it is a measure of producer welfare. It is measured as the difference between what producers are willing and able to supply a good for and the price they actually receive

thus producer surplus = p* q - ∫⁴₀ d(s) dp

= 7 * 4 - ∫⁴₀ 5p⁰°⁵ dp

= 28 - 5 ∫⁴₀ p⁰°⁵ dp

= 28 -5 *2/3 p¹°⁵

= 28 -5 *2/3 4¹°⁵

=$ 1.33

welfare from eliminating free trade

  • consumer price will increase
  • consumer surplus will decrease
  • import will decrease
  • reduced exports
  • portends gloom for the general outlook for the economy

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