Question

9.) Find the producer's surplus and the consumer's surplus for a product if its demand function is $p = 49 - x^2$ and it's supply function is $p = 4x + 4$. $CS = \int_0^x \text{demand } dx - \overline{p}x$ $PS = \overline{p}x - \int_0^x \text{supply } dx$

          9.) Find the producer's surplus and the consumer's surplus for a product if its demand function is $p = 49 - x^2$ and it's supply function is $p = 4x + 4$.

$CS = \int_0^x \text{demand } dx - \overline{p}x$

$PS = \overline{p}x - \int_0^x \text{supply } dx$

9.) Find the producer's surplus and the consumer's surplus for a product if its demand function is p = 49 - x^2 and it's supply function is p = 4x + 4.

CS = ∫0^x demand dx - px

PS = px - ∫0^x supply dx

Added by Gregory K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Pravin N

03/20/2022

Step 1

To find the equilibrium price and quantity, we need to set the demand function equal to the supply function and solve for x. Demand function: p = 49 - x Supply function: p = 4x + 4 Setting the two equations equal to each other: 49 - x = 4x + 4 Simplifying the Show more…

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9. Find the producer's surplus and the consumer's surplus for a product if its demand function is p = 49 - x and its supply function is p = 4x + 4. CS = 1/2 * (demand - price) * quantity PS = 1/2 * (price - supply) * quantity