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A box of Legos consists of complex bricks and basic bricks
A box of Legos consists of complex bricks and basic bricks. The production function of Lego boxes is assumed to be: Y=(B1(2/3)(2/3))x(B2(1/3)(1/3)) Where B1 denotes the number of basic bricks and B2 the number of complex bricks. Boxes of Legos are assembled in Denmark, combining these complex and basic bricks. Assuming that the Lego company optimizes its production, explain why the relative price of a complex brick relative to a basic brick should be equal to the ratio of marginal product of a complex brick over the marginal product of a basic brick.
Expert Solution
Let the price of basic brick be P1 and that of complex brick be P2.
The cost of production (C) and the production function is given below:
C=P1B1+P2B2Y=B123×B213C=P1B1+P2B2Y=B123×B213
To produce optimal quantity of output the price ratio of complex brick to basic brick should be equal to the ratio of marginal product of a complex brick over the marginal product of a basic brick. This is so because the price ratio of complex and basic brick is the slope of the cost function represented as isocost line and the ratio of marginal products is the marginal rate of substitution of two inputs used that are complex bricks and basic bricks which is the slope of the production function.
When we equate two slopes we get the optimum level of production which says that the combination of inputs that produce maximum output with the minimum input.
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