2 Suppose the demand for Digital Video Recorders DVRs is giv

2) Suppose the demand for Digital Video Recorders (DVRs) is given by Q=250 - .25p + 4pc, where Q is the quantity of DVRs demanded (in 1000s), p is the price of a DVR, and pc is the price of cable television. How much does Q change if the price of cable changes slightly (i.e. the partial derivative of demand with respect to pc)? Answer is: 4 please show step by step math process and explanation.

Solution

To calculate the partial derivative we take the derivative of the price of cable and assume all other variables as constant.

Now we know that the derivative of a constant is zero then

Q / Pc =(250)/Pc - (0.25p) / Pc + (4Pc)/ Pc

= 0 - 0 + 4

=4