F. Flinstone has quasilinear preferences and his inverse demand function for Brontosaurus Burgers is P(b)= 30-2b. Mr. Flintstone is currently consuming 10 burgers at a price of 10 dollars.

(a) How much money would he be willing to pay to have this amount rather than no burgers at all? What is his level of (net) consumer's surplus?
(b) The town of Bedrock, the only supplier of Brontosaurus Burgers, decides to raise the price from $10 a burger to $14 a burger. What is Flintstone's change in consumer surplus?

To answer these questions, we need to understand the concept of consumer surplus. Consumer surplus is the difference between the maximum price a consumer is willing to pay for a product and the actual price that they pay.

(a) To determine how much money Fred Flintstone would be willing to pay for 10 burgers instead of no burgers at all, we need to calculate his willingness to pay for those 10 burgers.

Given Fred Flintstone's inverse demand function: P(b) = 30 - 2b, where P(b) represents the price and b represents the quantity of burgers consumed.

We know that he is currently consuming 10 burgers at a price of $10, so we can substitute these values into the demand function:

P(b) = 30 - 2b
10 = 30 - 2(10)
10 = 30 - 20
10 = 10

From this calculation, we can see that the price he is currently paying is equal to his willingness to pay. Therefore, he would be willing to pay $10 to have this amount rather than no burgers at all.

To calculate his level of consumer surplus, we need to find the area of the triangle formed by his marginal willingness to pay (30 - 2b) and the actual price (10) for 10 burgers.

Consumer Surplus = (1/2) * Base * Height
Consumer Surplus = (1/2) * (10 - 0) * (30 - 20)
Consumer Surplus = (1/2) * 10 * 10
Consumer Surplus = 50

Therefore, his level of consumer surplus is $50.

(b) Now let's calculate the change in consumer surplus when the price increases from $10 to $14 per burger.

First, we need to calculate his new quantity demanded using the given inverse demand function:

P(b) = 30 - 2b
$14 = 30 - 2b
2b = 30 - $14
2b = $16
b = $8

So his new quantity demanded is 8 burgers.

To calculate the change in consumer surplus, we need to calculate the area of the new triangle formed by his new quantity demanded (8 burgers) and the difference in price (from $10 to $14).

New Consumer Surplus = (1/2) * Base * Height
New Consumer Surplus = (1/2) * (8 - 0) * (30 - 14)
New Consumer Surplus = (1/2) * 8 * 16
New Consumer Surplus = 64

The change in consumer surplus is the difference between the new consumer surplus and the previous consumer surplus:

Change in Consumer Surplus = New Consumer Surplus - Previous Consumer Surplus
Change in Consumer Surplus = 64 - 50
Change in Consumer Surplus = 14

Therefore, Fred Flintstone's change in consumer surplus is $14.

Since quasilnear preferences is a special case of a utility function Then...

u(x,y) = v(x) + y
Taking the derivative and setting to zero, a condition for maximizing utility is
v’(x) - p = 0 or p(x) = v’(x)
p(x) vs x as inv demand function