Question

An analyst believes that an increase in temperature by 1◦C decreases the demand for small coffee by .5%, holding everything else fixed. You may let T denote temperature in Celsius, and Q denote demand for a small coffee.

Does this statement mean the analyst believes that temperature causes demand to increase, or demand causes temperature to increase?

Write down an economic model, involving a specific equation, formalizing the statement at the beginning of the question. Please specifically use the number at the beginning of the question.

An American does not understand Celsius. Please repeat part (iii), but using Fahrenheit rather than Celsius. (The conversion is F = 32 + 9/ 5C.)

Answer 1

The analyst believes that an increase in temperature by 1◦C decreases the demand for small coffee by .5%, holding everything else fixed. This means that the temperature causes demand to increase if other factors are kept constant and not that demand causes temperature to increase.

Here demand of small coffee is dependent on temperature. Here demand is a function of temperature. It can be denoted as:

Q= f(T)

where Q is the demand for small coffee and T is the temperature in Celcius.

The equation explaining the statement that the analyst believes that an increase in temperature by 1◦C decreases the demand for small coffee by .5%, holding everything else fixed will be as follows:

Q- 0.5Q/100 = T+1

Where Q is the demand for small coffee and T is in the temperature in Celcius.

If the above equation is to be converted in Fahrenheit then it will be as follows:

Q-0.5Q/100=[( F-32) * 5/9 ] +1

Where Q is the quantity of small coffee and F is the Temperature in Fahrenheit.