Pyramid corporation is currently employing 20 tons of cement and 40 tons of steel to produce 50 000 square feet of shopping in a mall. Cement cost $20 a ton and steel cost $60 a ton. At the input quantities employed, MPc = 12 and MPs = 6.
1)show the situation in a Isoquent-isocost diagram.
2)is Pyramid corp. minimizing its long term costs?
3)if not what should it do if it wants to produce 50 000 square feet of shopping mall at minimum long term cost?Explain and show the diagram.
4)in the long run, what is the MRTS?
1) Cant really draw a graph here. But, put concrete on the y axis, steel on the x axis. With the current budget, the corporation can buy 3 times as much concrete as steel. Draw an isocost line with a slope -3. Now calculate the marginal rate of substitution in production. Two units of steel, at the margin, gives the same productivity as 1 unit of concrete. Draw an isoquant with a slope of 1/2. Both lines intersect at 20 cement, 40 steel.
2) obviously no.
3) If the marginal products are constant at all combinations of production, you will get a corner solution -- use only concrete. Otherwise more information is needed.
4) What is MRTS -- marginal rate of ??. Probably 3 tons concrete for 1 ton of steel.
1) To show the situation in an Isoquant-isocost diagram, you would need to plot the inputs, such as cement and steel, on the axes. The quantity of cement can be represented on the y-axis and the quantity of steel can be represented on the x-axis. Since the company is employing 20 tons of cement and 40 tons of steel, you would plot a point at (20, 40).
To draw the isocost line, you would calculate the total cost of the inputs employed. Cement costs $20 per ton, so 20 tons of cement would cost 20 * $20 = $400. Similarly, steel costs $60 per ton, so 40 tons of steel would cost 40 * $60 = $2400. The total cost of employing these inputs would be $400 + $2400 = $2800.
You can draw the isocost line by connecting the points that indicate the combinations of cement and steel that would cost $2800. For example, if cement costs $20 and steel costs $60, then you could have 40 tons of cement and 20 tons of steel.
The intersection of the isocost line and the isoquant (which represents the 50,000 square feet of shopping mall produced) would indicate the combination of inputs that are being used by the company.
2) Based on the information provided, it is not possible to determine if Pyramid Corp. is minimizing its long-term costs. In order to determine this, we would need to compare the cost of the current set of inputs to alternative combinations of inputs that can produce the same level of output. If the current set of inputs is the least costly option among these alternatives, then Pyramid Corp. would be minimizing its long-term costs.
3) To produce 50,000 square feet of shopping mall at minimum long-term cost, Pyramid Corp. would need to consider the marginal products and costs of the inputs employed. The marginal product of cement (MPc) is given as 12, while the marginal product of steel (MPs) is given as 6.
If the marginal products are constant at all combinations of production, then the firm would use only concrete to minimize costs. However, if the marginal products are not constant, more information would be needed to determine the optimal input combination. For example, if the marginal product of cement decreases as more cement is used, while the marginal product of steel increases as more steel is used, then the firm would need to find the point where the marginal products of the inputs are equal to each other. This point would represent the minimum long-term cost of producing 50,000 square feet of shopping mall.
4) The Marginal Rate of Technical Substitution (MRTS) represents the rate at which one input can be substituted for another while keeping the level of output constant. In this case, the MRTS would be the rate at which cement can be substituted for steel while maintaining the production of 50,000 square feet of shopping mall.
Based on the information provided, the MRTS can be calculated as the ratio of the marginal products of cement (MPc) to steel (MPs). In this case, the MRTS would be 12/6 = 2 tons of cement for 1 ton of steel.