In the past 30 years the price of robots has fallen by 50% in real terms, a McKinsey survey has found. Using the cost minimization model, show what impact the relative drop in the per unit price of robots has on the choice of the quantities of labor and robots to be used to produce a desired level of output.

Assume that the per unit price of robots is r, the per unit price of labor is w, and total cost is equal to C=wL+rR

Where L is the quantity of Labor and R is the quantity of Robots.

In your graph you should be clear in labelling both your X (Labor) and Y (Robot) axis, the relevant intercepts in symbol form with the appropriate subscripts to denote which variables have changed versus which have stayed constant.

After drawing your graph showing the initial cost minimizing quantities of L and R at the initial set of relative input prices, draw in the same graph what happens as the relative price of robots falls. Show all three isocost lines and the single isoquant in your graph. The first isocost line should depict the original tangency at the initial set of relative input prices (before r falls).

The second isocost line should show the impact of r falling, holding total cost and w constant, and the final isocost line should depict the final isocost line that allows the firm to produce the desired output at the new set of relative prices.

Be clear to talk about what has happened in your graph-how the cost minimizing amounts of labor and robots has changed as a result of the per unit price of robots falling, holding w constant.

Is the result you showed in your graph consistent with what you have observed in some firms? Give a real-world example and discuss - just a few sentences.