How an Increase in Price of Substitutes and Monthly Income Affects Demand for ACME Widgets

(a) How does an increase in the price of substitutes and monthly income affect the demand for ACME Widgets?

In this case, ACME Widgets can increase their price by how much to maintain demand at 4700 units/month?

(b) What will be the change in ACME's monthly revenue if they increase the price?

Answer:

To determine how an increase in the price of substitutes (ps) and monthly income (Y), with no change in price (p), affects the demand for ACME Widgets, we can utilize the provided partial derivatives.

From the given data, we can calculate the changes in demand when the price of substitutes (ps) increases to 9.32 and monthly income (Y) increases to 5.4, while the price (p) remains unchanged at 10. The partial derivatives ∂q/∂ps = 0.75 and ∂q/∂Y = 0.26 indicate the responsiveness of demand to changes in ps and Y, respectively.

When ps increases to 9.32, the demand for ACME Widgets is estimated to increase by approximately 0.24 units (in thousands). Similarly, with an increase in monthly income to 5.4, the demand is expected to rise by around 0.104 units (in thousands).

To maintain the demand at 4700 units/month, ACME can increase the price (p) by approximately $9.79 according to the given partial derivative ∂q/∂p = -0.48. This price adjustment would enable ACME to sustain the monthly demand at the desired level.

Since the revenue function is not provided in the data, the precise change in ACME's monthly revenue cannot be directly calculated. The revenue would be influenced by the price changes and the corresponding demand adjustments due to those price changes.