3. Assume you are trying to estimate the demand for running shoes. You believe t

Question

3. Assume you are trying to estimate the demand for running shoes. You believe that the quantity demanded is a function of the price of running shoes (P), advertising expenditures (ADS), and whether individuals exercise or not (EX). Whether people exercise (EX) takes on a value of one when people exercise and is equal to zero otherwise. A. (1 Poi demand lin nt) Construct a general demand equation that assumes all three variables enter early. Use generic B, values to represent the coefficients on each of your variables. r constant and then B, through B on each of the variables in the order they are listed at the beginning of the problem. Price should have its usual sign. Increased advertising expenditure should increase demand. The decision to exercise should increase demand but not have a role in the effect advertising has on demand. B. (2 Points) Assume you want to calculate the elasticity of demand with respect to advertising expenditures. Your calculation will require an element representing AQ/AADS. State two different values for aaADS. Your first value SHOULD NOT allow the effect of advertising expenditures to vary by the decision to exercise. Your second value SHOULD allow the effect of advertising to vary by the decision to exercise. (HINT: your answers will be in terms of some or all of the Bivalues).

Explanation / Answer

Consider the given problem here “Q=Quantity of Running Shoes”, “P=Price of Running shoes”, “ADS=Advertising Expenditures” and “Ex=Exercise”. So, here the “EX” is dummy variable takes “1” if a typical individual “exercise” and takes “0” if not “exercise”.

So, here the demand function for “Running Shoes” with the help of above information given in the question, is given by.

=> Q = b0 - b1*P + b2*ADS + b3*EX*ADS.

b).

Now, to find out the elasticity of “demand” with respect to “ADS” we need to find out “dQ/dADS”. Now, the demand function is given by as follows.

=> Q = b0 - b1*P + b2*ADS + b3*EX*ADS, by differentiating with respect to “ADS” we have the following condition.

=> dQ/dADS = b2 + b3*EX.

Now, 1st if “values should not allow the effect of ADS to vary by the decision to exercise”, => “Ex=0”, => the above expression will be “dQ/dADS = b2 > 0”.

Similarly, 1st if “values should allow the effect of ADS to vary by the decision to exercise”, => “Ex=1”, => the above expression will be “dQ/dADS = b2 + b3 > 0”.

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