Philip is planning to allocate his allowance between jam and honey. If he decides to spend all his money on jam, he could afford 14 jars of jam. Philip's preferences for jam (J) and honey (H) are given by the following utility function: (, ) = 2 + 0.5 2 ( = 2, = 2 + ). Philip's optimal consumption choice implies he buys 6 jars of jam and 4 jars of honey. The price of a jar of honey is 5.

a) Calculate Philip's total allowance and the price of jam. Write down his budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis.

b) Calculate Philip's marginal rate of substitution between jam and honey at his optimal consumption bundle. Explain the concept of MRS and interpret the figure obtained.

c) Show Philip's optimal consumption bundle in the adequate graph. Explain your reasoning.

d) Show, both algebraically and graphically, how Philip's optimal consumption choice would change if his allowance is reduced by 20%.

e) Discuss how Philip's demand for jam/honey can be obtained. Based on your analysis of questions a-d, can you conclude whether jam is a normal/inferior/Giffen good to Philip? How about honey?