Question

Taco Corp. is trying to decide the lowest cost way to produce 500 new apartments. Currently they are using 10 acres of land (L) and 50 tons of concrete (C). Land costs $4,000 an acre and concrete costs $12 per ton. For the input amounts being used, MPL = 50 and MPC = 4. Show this situation in an isoquant-isocost diagram. Explain what is going on in the diagram and discuss how Taco can produce the same output at a lower total cost.

Answer 1

Ans. Marginal Rate of Technical Substitution, MRTS = MPL/MPC = 50/4 = 12.5
At cost minimizing level of output,

MRTS = Land Cost/Concrete Cost

Here, Land Cost/ Concrete Cost = 4000/12 = 333.33

So, here, MRTS < Land Cost/Concrete Cost

So, marginal product per dollar for land is less than marginal product of concrete per dollar, so, cost if production of 500 apartments can be minimized by increasing consumption of concrete and reducing consumption of land.

On the diagram,

First the isoquant was IQ1 at which the consumption bundle was (10, 50) producing at isocost line IC1 with cost $40600 (=4000*10 + 12*50)

If the consumption of concrete is increased and land is decreased to produce same amount, 500 apartments, this would lead to movement upward on the isoquant to the new point where IQ1 is tangent to the new isocost line IC2 with lower total cost.