I'm having trouble figuring out how to calculate these questions and what formulas to use for these practice questions, The inverse demand curve for a product using resource X is given by P 200 0 5Q and the cost of production is constant at MC 25 a Find the static equilibrium for this product in a single time period (call this t 0 ) (recall at equilibrium Supply equates Demand and in this case Demand or Price Marginal Cost) b What is the value of consumer surplus from consumption in t 0 (recall, this is simply the area under the demand curve and above the price, which now equates Marginal Cost) Imagine that resource X is infinite in supply or perfectly renewable and that the demand and supply curves are unchanged between years c How much would be produced consumed in the following year (called t 1 ) Because Marginal Cost is constant in this example, it is possible to simply subtract MC from the demand curve to establish the Net Marginal Benefits (i e the Consumer Surplus) in each time period This effectively creates a Net Marginal Benefit curve that shifts downwards from the initial demand curve but remains parallel Thus, the Net Marginal Benefits are given by NMB 200 0 5Q 25 175 0 5Q Now imagine that there is not enough of resource X to support the static efficient consumption in both time periods (i e t 0 and t 1 ) More specifically, assume that the total stock available in both periods is 600 units d How much is consumed in t 0 e How much is left to consume in t 1 You may find this distribution is quite uneven with most consumption occurring in t 0 f Assume a discount rate of 8 , how much is the NMB of the following year (period t 1 ) (note that you need to discount the future value of NMB in period t 1 into a present value) Hint take the NMB formulae for t 1 assumed the same as for t 0 and divide by the factor 1 08 (because the discount rate is 8 ) Now that you have the NMB for t 1 you should be able to solve for the dynamically efficient output and consumption between the two time periods Remember that to be dynamically efficient the MNB in t 0 must equal the discounted MNB for t 1 (Hint this is done algebraically by setting the two equations equal and solving for Q The solution for Q is the amount consumed in t 0 so the difference between this and 600 is the amount consumed in t 1 ) g What is the dynamically efficient consumption production in t 0 h What is the dynamically efficient consumption production in t 1 i When future benefits are discounted, is the dynamically efficient consumption of the current generation higher or lower than that which occurs without discounting

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jun 24, 2024

I'm having trouble figuring out how to calculate these questions and what formulas to use for these practice questions, The inverse demand curve for a

I'm having trouble figuring out how to calculate these questions and what formulas to use for these practice questions,

The inverse demand curve for a product using resource X is given by P = 200-0.5Q and the cost of production is constant at MC = 25.

a.Find the static equilibrium for this product in a single time period (call thist₀) (recall at equilibrium Supply equates Demand and in this case Demand or Price = Marginal Cost).

b. What is the value of consumer surplus from consumption int₀? (recall, this is simply the area under the demand curve and above the price, which now equates Marginal Cost)

Imagine that resource X is infinite in supply or perfectly renewable and that the demand and supply curves are unchanged between years.

c.How much would be produced/consumed in the following year (called t₁)?

Because Marginal Cost is constant in this example, it is possible to simply subtract MC from the demand curve to establish the Net Marginal Benefits (i.e. the Consumer Surplus) in each time period. This effectively creates a Net Marginal Benefit curve that shifts downwards from the initial demand curve but remains parallel.

Thus, the Net Marginal Benefits are given by NMB = 200 - 0.5Q - 25 = 175 - 0.5Q

Now imagine that there is not enough of resource X to support the static efficient consumption in both time periods (i.e.t₀andt₁). More specifically, assume that the total stock available in both periods is 600 units.

d. How much is consumed in t₀?

e. How much is left to consume int₁?

You may find this distribution is quite uneven with most consumption occurring int₀.

f.Assume a discount rate of 8%, how much is the NMB of the following year (periodt₁)? (note that you need to discount the future value of NMB in periodt₁into a present value).Hint: take the NMB formulae fort₁- assumed the same as fort₀- and divide by the factor 1.08 (because the discount rate is 8%).

Now that you have the NMB fort₁you should be able to solve for the dynamically efficient output and consumption between the two time periods. Remember that to be dynamically efficient the MNB int₀must equal the discounted MNB fort₁. (Hint: this is done algebraically by setting the two equations equal and solving for Q. The solution for Q is the amount consumed int₀so the difference between this and 600 is the amount consumed int₁).

g. What is the dynamically efficient consumption/production int₀?

h. What is the dynamically efficient consumption/production int₁?

i.When future benefits are discounted, is the dynamically efficient consumption of the current generation higher or lower than that which occurs without discounting?