We need to build a new prison in the county that meets the requirement of holding 2 prisoners in 50 square feet, with a capacity of 200 prisoners. In total, this implies 1,000 square feet. We could build it "wide" (few floors that are very large) or "tall" (small floors stacked upon each other). As we build "wider" we use more land. If we use less land, then we add more capital to construct them tall. We don't have to finish every floor, so we can have fractional floors. Here is a table of some options that are able to build 2,000 square feet of space: Option Blocks of Land Floors 4 2 1.33 1- Which tool of the production choice decision framework is on display in the table? A. An isaquart B. An Isocast or budget curve C. Economies of scale D. Economies of scope Speaking of that tool, it has a slope known as the marginal rate of technical substitution. If we plotted it on a diagram where Blocks is on the y-axis and Floors is on the x-axis, then the Marginal Rate of Technical Substitution of Floors for Blocks is: MRTS=MP of floors / MP of blocks We're going to assume a very specific type of output mapping so that you can get this marginal product ratio by calculating the change in Floors versus change in blocks of land. The MRTS of B is -0.667 (i.e. you will save the production of .67 floors by adding one block of land). 2- What is the MRTS of option A? 3- What is the MRTS of option C? Suppose each block of land costs $1 million and each floor costs $2 million. Option A has a total cost of $9 million. Figure out the total cost of each option. 4- Which was the least expensive? You have the MRTS of A and C already, the MRTS of B is -0.667 (i.e. you will save .67 ). The previous question with total costs tells you that: Price of floors/price of blocks = 2mill/1mill=-2 The cost minimizing solution will gravitate towards a solution where MRTS=ratio of prices. So lets look at option B: -0.667 vs. -2 Since for Option B MRTS>ratio of prices, it implies that the marginal product savings of moving to Option C will be justified on the basis of cost savings, so we should now explore Option C. Option C will fail to justify considering Option D. If you went back and looked at Option A, it would imply you should consider Option B. You previously found the cost minimizing option when land blocks cost $1 million and floors cost $2 million each: 5- The cost minimizing option would be the same if land blocks cost $2 million and floors cost $4 million each? True False You previously found the cost minimizing option when land blocks cost $1 million and floors cost $2 million each: 6- The cost minimizing option would be the same if land blocks cost $0.5 million and floors cost $1 million each? True False You previously found the cost minimizing option when land blocks cost $1 million and floors cost $2 million each: 7- The cost minimizing option would be the same if land blocks cost $2 million and floors cost $1 million each? True False