Question

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

Answer 1

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

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