The solution provided is based on the principle of dynamic efficiency for a depletable resource, where the goal is to maximize the present value of the net benefits from the resource. Here's a step-by-step explanation of the solution: The inverse demand function is given as P=25-0.4q, where P is the price and q is the quantity. The marginal supply cost (MSC) is constant at £5. The total quantity to be allocated is 40 units, and it needs to be divided between two periods, period 1 and period 2. To find the dynamic efficient allocation, we equalize the present value of the marginal net benefits (MNB) from each period, which is the price minus the marginal cost. The present value of the marginal net benefits for each period can be expressed as: • For period 1: PV(MNB1)=(25-0.4q1-5)(1+r) • For period 2: PV(MNB2)=(25-0.492-5) Because the total benefit must be maximized over both periods, we set PV(MNB1) equal to PV(MNB2), and solve for 1q1 and q2 with the constraint that q1+q2=40. The equation to be solved is (1+r)=25-0.4q2-5, where r is the discount rate (0.15 in this case). To solve for q1 and q2, we manipulate the equations as follows: •Expand the left side: 20(1+0.15)-0.4q1 (1+0.15)=20-0.4q2 • Simplify both sides: 23-0.46q1-20-0.4q2 By substituting the constraint q2=40-q1 into the equation, we solve for q1 and then use it to find q2. The result of this process gives the allocation of the resource to each period. The calculated allocation is approximately 14.44 units for period 1 and 25.56 units for period 2. This C C 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

What is the conditional demand for input 1? Use cost function c(w1;w2; y) = w11/2w21/2y2

4. Find the cost function and the conditional demands for inputs associated to the CES production function f(r1, #2) = A(ar{ + (1 – a)a)/e, where A, 8 > 0, 0 < a < 1, and 0#p< 1.

The constraint for a given resource is given by the following equation: 2X₁ +3X₂ ≤20. If X₁ = 2 and X₂ = 3, how many units of this resource are unused? 0 20 04 07

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)

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…

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?

Suppose we allocate a fixed supply of a depletable resource between two periods in a dynamically efficient way. Assume further that the demand function is constant in the two periods and the marginal willingness to pay is given by the formula P = 8 - 0.35q while the marginal cost is constant at $1 per unit. The total supply is 21 units and the discount rate is 2%. What is the marginal user cost during the first period?

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)

Business Unit A, the supplying business unit, is selling to an outside market. It has excess capacity and can use it to transfer product to the receiving business unit, Business Unit B. Business Unit A does not incur incremental fixed costs in the production of the units supplied to Business Unit B. The formula to calculate the transfer price in this scenario is:? a. (Total variable costs + incremental fixed cost) ÷ total units supplied b. (Total variable costs + Contribution margin lost) ÷ total units supplied c. (Total variable costs + incremental fixed costs + Contribution margin lost) ÷ total units supplied d. Total variable costs ÷ total units supplied