Suppose the inverse demand function for a depletable resource is linear, P = 25 – 0.4q, and the marginal supply cost is constant at £5.i. If 40 units are to be allocated between two periods in a dynamic efficient allocation, how much would be allocated to period 1 and how much to period 2 when the discount rate is r = 0.15? Show your working ii. What is the marginal user cost in each period? Provide a one-sentence economic interpretation iii. Show in a diagram how the marginal user cost would change if an energy price shock were to raise the marginal cost in period 2 to £10

The market for gravel has the following demand and supply relationships: Supply function: Q = 100P - 1,000 Inverse demand function: P = 50 - 0.01*Q + PX, where P represents price of gravel per ton in dollars, Q represents sales of gravel per week in tons, and PX is the price of some other product X in dollars per unit. Let PX = $50/ton In a diagram, qualitatively describe the change that would occur in the market for gravel (i.e. equilibrium price and quantity) if a new discovery has just made the production of product X cheaper. Briefly explain whether it is a movement along or shift of demand curve and supply curve for gravel. In addition to the new discovery regarding product X in previous question), suppose now workers producing gravel ask for sick leave due to COVID. Use supply and demand analysis to predict how these two shocks will affect equilibrium price and sales. Illustrate your results in a diagram. Is there enough information to determine if market prices will rise or…

For the manufacturing company in problem 1, let the prices of input 1 and 2 be w₁ = 10 and w₂ = 40, respectively. (A) Find the amount of each input to hire to minimize the cost of producing y = 100 units of output: min C (x1, x2) = 10x1 +40x2 subject to: 10x12x1/2 = 100

In the answer below to my question which is also attached, how is the equation solved? r is given but i don't see how you can solve for q1 and q2 with the equation (25-0.4q1-5)(1+r) = 25-0.4q2 -5 = λ

Why hasn't the depletion of nonrenewable resources happened as predicted? Do the pricing signals at this time indicate that nonrenewable resources are almost exhausted?

Green et al. (2005) estmate the supply and demand curves for Californa processod tomatoes. The supply function is: \[ \ln \left(Q_{s}\right)=0.200+0.550 \ln (p) \] whereQis the quantify of processing tomatoes in milions of tons per year andpis the price in dollars per ton. The demand function is: \[ \ln \left(Q_{d}\right)=2600-0.200 \ln (p)+0.150 \ln \left(p_{1}\right) . \] wherep1​is the price of tornato paste (which is what processing tomatoes are used to produce) in dollars per ton. Supposept​=$119Determine how the equilerium price and quantity of processing tomatees change if the price of tomato pasise tails by16%. If the price of tomato paste fals by18%, then the equaborium price will by 5 (Enter a numene response using a real number rounded to two decimal places)

dien There are two factors in a production function y = x 113 x₂¹1³. The market price of each unit ofy is p=3, and the factor prices are w₁=1 and W₂=2 for x₁ and X₂ respectively. variable (a). Calculate your cost function as a function of y if X, and x₂ are both barible factors. (b). Now derive the functions of average and marginal cost and plot them against quantity (C). Solve for your optional output of y. Calculate the ratio of two factors (X₁/X₂) (d). In the short run the fixed factor is set at X₂=1. What is the new optimal output level now?

1) Assume the production process can be represented by the following production function: Q=4K¹/²¹/2 We are operating in the short-run and thus K is fixed. We currently have use of 16 units of K. Note that the wage is $200 per worker, the rental rate of K is $150 per unit, and our output sells for $100 per unit. a) Write an expression for the MPL in the short-run:

Calculate the Lagrange multiplier of the cost minimization problem with a CobbDouglas production function, and show that it is equal to the derivative of the costfunction with respect to output (the marginal cost)

b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L and K can vary with production. Compute the input demand functions as a function of Q. (4 Points) c Calculate the marginal cost and average cost of the above function in subpart (b). Show them graphically. At what prices of textile will the producer shut down production. (3 Points) d Now suppose Q = 10LK. The market prices of inputs are as in subpart (b) above. Compute the input demand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn. (5 Points)