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 DeltaCS) from eliminating free trade is $ nothing. (Enter your resp

$52

$ 1.33

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

answer; a large down payment,a longer term loan, would result in a lower monthly payment;