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- If Q equals the level of output, P is the selling price per unit, V is the variable cost per unit, and F is the fixed cost, then the break-even point in units is: a Q ÷ (P − V). b F ÷ (P − V). c V ÷ (P − V). d F ÷ [Q(P − V)].In the cost behavior equation, b*X denotes the variable cost per unit. Select one: O True O FalseYou are the principal economist at a firm that produces some output y based on the following function: y = f(x1, x2) = x ³ x ² 1. Calculate the marginal product (MP) of both inputs at some arbitrary input bundle (x₁, x₂). Interpret the sign of both. 2. Using your answer in the previous part, calculate OMPT₂/0x₁. Interpret what this means. 3. Calculate the technical rate of substitution between ₁ and x2, i.e., MP/MP₂. 4. Does this production function exhibit increasing, decreasing, or constant returns to scale? Show. 1 5. Lay out a brief, realistic example of x₁, x2, y that fits the dynamics that you calculated.
- Suppose that there is a constant technological progress (A) and population growth (n) in a sample economy. Production function is given as Y, = F(Kt, N¿) = A/K/N. a) Write the output per worker as a function of capital per worker.Find the marginal profit function if cost and revenue are given by C(x) = 224 + 0.8x and R(x) = 8x – 0.05x2. P'(x) =D2) What is measured along the horizontal axis in a graph of the production possibility frontier? the amount of labor input the amount of capital input the quantity of one good produced the quantity of one good exported
- Within the relevant range: Select one: O A. variable cost per unit decreases as production decreases. O B. fixed cost per unit increases as production decreases. O C. fixed cost per unit decreases as production decreases. O D. variable cost per unit increases as production decreases.The supply and demand equations of a good are given by the following formulas P=2Qs +48 P= -6QD+ 160 Find the equilibrium price and quantity. The equilibrium quantity is. (Type an integer or a decimal.) ***Which of the following is not an assumption of the basiceconomic-order quantity model?A. quantity discounts are availableB. ordering or setup costs are constantC. lead time is constantD. annual demand is constant and know
- Suppose the representative firm of the economy has a production function of the form F(K, N) =AK0.5N 0.5 . The marginal product of labor is then given by MP N = 0.5AK0.5N −0.5 . The current capitalstock is K = 40. (a) Holding fixed capital at 40, draw a graph of output as a function of labor. What are some importantfeatures of this graph? (b) If A = 4 what is the Labor Demand Curve, ND(w), as a function of the real wage w? (c) Suppose labor is supplied inelastically with NS(w) = 10. What is the equilibrium wage w, employmentlevel N, and full employment output Y ? (d) Suppose that productivity unexpectedly increases to A = 6. What is the new equilibrium wage w,employment level N, and full employment output Y ?On a CVP graph, the total cost line intersects the vertical (dollars) axis at a. the origin. b. the level of the fixed costs. c. the breakeven point. d. the level of the variable costs.The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form: f(L,C)=c0Lc1Cc2, where c0, c1, and c2 are constants. The variable L represents the units of input of labor, and the variable C represents the units of input of capital. a. In this example, assume c0 = 5, c1 = 0.25, and c2 = 0.75. Assume each unit of labor costs 25 and each unit of capital costs 75. With 75,000 available in the budget, develop an optimization model to determine how the budgeted amount should be allocated between capital and labor in order to maximize output. b. Find the optimal solution to the model you formulated in part (a). (Hint: When using Excel Solver, use the Multistart option with bounds 0 L 3,000 and 0 C 1,000.)