This paper provides a simple example of the utility function with two consumption goods which can be calculated by hand to produce a Giffen good. It is based on the theoretical result by Kubler et al. (Am Econ Rev 103:1034–1053, 2013). Using a model of portfolio selection with a risk-free asset and a risky asset, they showed that there always exists a parameter set which assures that the risk-free asset becomes a Giffen good if the utility function belongs to the HARA (hyperbolic absolute risk aversion) family with decreasing absolute risk aversion (DARA) and decreasing relative risk aversion (DRRA). This paper investigates their result further in a usual microeconomic setting where the risk-free asset and the risky asset are changed to the first and second consumption goods, respectively. It is organized as follows. First, a standard utility maximization problem of a consumer is directly solved to obtain the conditions for the first good to be a Giffen good. Second, the same problem is analyzed by means of decompositions of the price effect due to Slutsky and Sasakura (Italian Econ J 2:258–280, 2016). As is well known, the former decomposition consists of the substitution effect and the income effect, while the latter implies the decomposition into the ratio effect and the unit-elasticity effect. Lastly these analyses are compared and summarized. It should be added that the utility function proposed in this paper can also be used for the analysis of a normal good mutatis mutandis.

本文提供了一个实用函数的简单示例，其中有两个可以手动计算的消费品生产吉芬产品。它基于Kubler等人的理论结果。（Am Econ Rev 103：1034–1053，2013）。使用具有无风险资产和风险资产的投资组合选择模型，他们表明，始终存在一个参数集，如果效用函数属于HARA（双曲线绝对风险），则可以确保无风险资产成为吉芬商品。减少绝对风险规避（DARA）和相对风险规避（DRRA）的家庭。本文在通常的微观经济环境中进一步研究了它们的结果，在该环境中，无风险资产和风险资产分别更改为第一和第二消费品。它的组织如下。首先，直接解决消费者的标准效用最大化问题，以获得第一商品成为吉芬商品的条件。其次，通过分解因Slutsky和Sasakura造成的价格效应来分析相同的问题（意大利经济杂志J 2：258–280，2016）。众所周知，前者的分解包括替代效应和收益效应，而后者则意味着分解成比例效应和单位弹性效应。最后，对这些分析进行了比较和总结。应该补充的是，本文提出的效用函数也可以用于正常商品的分析。最后，对这些分析进行了比较和总结。应该补充的是，本文提出的效用函数也可以用于正常商品的分析。最后，对这些分析进行了比较和总结。应该补充的是，本文提出的效用函数也可以用于正常商品的分析。经过必要修改。